If all the sides of a parallelogram touch a circle, then the parallelogram is
If all the sides of a parallelogram touch a circle, then the parallelogram is a rhombus.
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True or False: The product of two negative integers is a negative integer.
False. The product of two negative integers is always a positive integer.
Multiply 2x + 5 and 4x + 3.
(2x + 5) (4x + 3) = 8x2 + 6x + 20x + 15 = 8x2 + 26x + 15
Define an equilateral quadrilateral.
An equilateral quadrilateral consists of all the sides that are equal in length.
A number that has more than two factors is called a
A number with more than two factors is called a composite number.
What is the compounded ratio of 10 : 30 and 60 : 80?
Compound ratio = (10 / 30) * (60 / 80) = 1 / 4 Hence, the ratio is 1 :... View Article
Represent the complex number z = 1 + i in polar form.
r = √2 and θ = π / 4 The polar form is √2 (cos π / 4 + i... View Article
A perfect cube does not end with two zeros. – True or False
The given statement is true. A perfect cube does not end with two zeros.
Six coins are tossed simultaneously the probability of getting at least 4 heads is
Probability is a branch of mathematics that deals with the occurrence of a random event. The probability formula is defined... View Article
Without actually calculating the cubes, find the value of each of the following: (28)3 + (− 15)3 + (− 13)3.
The given expression is (28)3 + (− 15)3 + (− 13)3. \(\begin{array}{l}\text { If }(a+b+c)=0, \text { then } a^{3}+b^{3}+c^{3}=3... View Article
Prove (1 + cos A) / sin A + (sin A) / (1 + cos A) = 2 cosec A.
Consider the LHS of the given expression. \(\begin{array}{l}\text { L.H.S. }=\frac{1+\cos A}{\sin A}+\frac{\sin A}{1+\cos A} \\ =\frac{(1+\cos A)(1+\cos A)+\sin A... View Article
Evaluate the following using suitable identities 1053.
The given number can be expressed as \(\begin{array}{l}\Rightarrow(105)^{3}=(100+5)^{3}\\ (a+b)^{3}=a^{3}+b^{3}+3 a b(a+b) \\ a=100, b=5\\ \Rightarrow(105)^{3}=(100)^{3}+(5)^{3}+3 \times(100) \times(5) \times(100+5)\\ n=3, x^{n}=\underbrace{x... View Article
Solve sin 10 + sin 20 + sin 40 + sin 50.
sin 10 + sin 20 + sin 40 + sin 50 = (sin 10 + sin 50) + (sin 20... View Article
What per cent of 90 is 120?
Consider a number to be x. x% of 90 is 120 x% × 90 = 120 (x /100) × 90... View Article
Fill in the blanks: The greatest 4 digit number with 3 different digits is
The greatest 4 digit number with 3 different digits is 9987.
The additive identity of any rational number is
0 is the additive identity of any rational number.
Solve (x / 2) – (x / 3) = 8 explain.
(x / 2) – (x / 3) = 8 8 = [x . 3] / 6 – [x . 2]... View Article
The value of the derivative of |x − 1| + |x − 3| at x = 2 is:
|x| = x for all x ≥ 0 |x| = − x for all x < 0 When x =... View Article
How many days are there in x weeks x days?
x weeks x days = (7x + x) days = 8x days
Tossing a coin is an example of
Tossing a coin is an example of an experiment.
